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I have the following information:

Measure A had a Pearson correlation of 0.60 with measure B in one sample.

The two-week test-retest reliability of measure A in the same sample was 0.64. The two-week test-retest reliability for measure B was 0.76 (Pearson correlation of the sum scores for both).

Say I now have a third measure administered to this sample, measure C. Measures C and B are both depression symptom scores. Given the two-week test-retest reliability for B, we can be confident that depressive symptoms are reasonably stable over two weeks. Measures B and C have been psychometrically validated in other literature (proved concurrent validity against structured clinician interviews, analyzed factor structure, etc).

Measure C was administered within 2 weeks of measure A. Its correlation with measure A is only 0.30. So, measure C was administered at a different time to A, and it is similar to B in nature. However, I don't have the correlation between B and C in this sample (still searching for papers that reported correlations between these measures in other samples).

Is there a way to guesstimate the expected correlation between A and C, e.g. by multiplying the concurrent correlation of A and B and the two-week test-retest correlation of B?

(Yes, I know this would involve a lot of assumptions, but I emphasize I am looking for a guesstimate of the correlation I can expect between A and C; 0.30 is low, but I want to account for the fact that the test differs and the administration time differs.)

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In path model analysis, the correlation between two variables connected via a third variable is calculated in this fashion. For example, if $A \rightarrow B$ has a standardized coefficient of 0.6 and $A$ and $C$ are correlated 0.5, then the (standardized) indirect relationship between $C$ and $B$ (thru $A$) is $0.6 \times 0.5= 0.3$. The total correlation would be this value added to the values from any other valid paths in the model. Assuming none (mainly, assuming no direct path from $C$ to $B$), this would be the correlation between those two variables.

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    $\begingroup$ That sounds good. I was not familiar with path model analysis. Thanks! $\endgroup$
    – Weiwen Ng
    Commented Apr 6, 2018 at 20:00

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